{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stacks Overview\n",
    "\n",
    "**Please see the lecture video for the full Overview on Stacks!**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "____\n",
    "\n",
    "A stack is an ordered collection of items where the addition of new items and the removal of existing items always takes place at the same end. This end is commonly referred to as the “top.” The end opposite the top is known as the “base.” \n",
    "\n",
    "The base of the stack is significant since items stored in the stack that are closer to the base represent those that have been in the stack the longest. The most recently added item is the one that is in position to be removed first. \n",
    "\n",
    "**This ordering principle is sometimes called LIFO, last-in first-out.** It provides an ordering based on length of time in the collection. Newer items are near the top, while older items are near the base.\n",
    "\n",
    "For example, consider the figure below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9DUCzevbs6efnt2rVKmqDHH377bfqq+5BolgkqnW+BVEdgGjwV3fTIA+BvgmH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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "url ='https://upload.wikimedia.org/wikipedia/commons/b/b4/Lifo_stack.png'\n",
    "\n",
    "Image(url)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note how the first items \"pushed\" to the stack begin at the base, and as items are \"popped\" out. Stacks are fundamentally important, as they can be used to reverse the order of items. The order of insertion is the reverse of the order of removal.\n",
    "\n",
    "Considering this reversal property, you can perhaps think of examples of stacks that occur as you use your computer. For example, every web browser has a Back button. As you navigate from web page to web page, those pages are placed on a stack (actually it is the URLs that are going on the stack). The current page that you are viewing is on the top and the first page you looked at is at the base. If you click on the Back button, you begin to move in reverse order through the pages.\n",
    "\n",
    "In the next lecture we will implement our own Stack class!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Extra Resources:\n",
    "[Wikipedia Page on Stacks](http://bit.ly/1OJybGQ)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
